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Find the median of the following data: 12, 25, 95, 30, 25, 36, 98, 85, 54, 42.
36
38
39
42
39
Count the total number of terms (n=10), mentally arrange them in order, and identify the middle two terms (5th and 6th positions) then take their average.
A set of data values: 12, 25, 95, 30, 25, 36, 98, 85, 54, 42.
Median=2(2nтАЛ)thterm+(2nтАЛ+1)thtermтАЛ
Count the total number of terms (n=10), mentally arrange them in order, and identify the middle two terms (5th and 6th positions) then take their average.
Most students forget to sort the data set in ascending order before picking the middle value, leading to an incorrect result.
Sort the data
Arrange the given 10 numbers in ascending order: 12, 25, 25, 30, 36, 42, 54, 85, 95, 98.
12,25,25,30,36,42,54,85,95,98
Identify terms
Since the number of observations n=10 (which is even), the median is the average of the 5th and 6th terms.
n=10,5th┬аterm=36,6th┬аterm=42
Calculate Median
Calculate the mean of the 5th and 6th terms to find the median value.
Median=236+42тАЛ=278тАЛ=39
C is correct because the average of the 5th and 6th terms in the sorted sequence is 39.
This concept is fundamental to Probability and Data Interpretation; remember that for grouped data, you use the Median Class formula.
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